Bohr–van Leeuwen theorem – magnetism in solids is a quantum mechanical effect | Hacker News Reader

Bohr–van Leeuwen theorem – magnetism in solids is a quantum mechanical effect

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Neither can even basic chemistry. Intro to chemistry is sort of just a giant hint at quantum mechanics. When you get into electron shell configurations, inevitably there will be a student who will ask why electrons arrange themselves like this. The teacher will say "well, it's complicated". But it's just basic quantum mechanics. I wish they would have explained the concepts at least. Obviously the math is complicated but the ideas really aren't too bad.

I’d love to read more. Can you or someone else provide a relevant link?

Well classically, atoms wouldn’t even be stable. Their electrons would radiate energy when orbiting and therefore spiral into the nucleus. So without quantum physics you don’t have fundamental properties of atoms like energy levels which explains their chemical properties.

> Their electrons would radiate energy when orbiting

What phenomenon would make them lose energy?

Under the assumption that the electron is a point charge moving in a circular path, it radiates electromagnetic energy as it moves, in the form of field ripples.

This gif is for a 1d oscillation rather than an orbit, but it does a good job of conveying the idea.

https://thumbs.gfycat.com/ExhaustedAlarmedDeinonychus-size_r...

Interestingly enough, if the electron were a continuous ring (like Saturn's rings) rather than a point charge, it could orbit without losing energy, generating only a static magnetic field. I don't know why this model rarely comes up in explorations of classical physics models of the atom.

I remember I once found a website that started by simply explaining that all electron orbitals are quantised because there must be an whole number of waves an electron would make around the orbital or otherwise the wave function would start cancelling itself (and thus this energy has got to go somewhere).

This sounds a bit like old quantum theory: https://en.wikipedia.org/wiki/Old_quantum_theory

I'd say the intuition here is misleading. S orbitals (including the ground state) really are spherically symmetric. There are no waves "around" the orbital: they only vary in the radial direction.

But "must smoothly connect" is important. As you walk outwards from the nucleus, the electron wavefunction oscillates until it reaches the classical turning point, when it switches to exponential decay. Only a very few functions can smoothly join these two modes, which is one explanation for why bound state energies are quantized.

I think it only depends on how you visualise the wave function.

In that case the drawing was 2-dimensional, but the wave function was defined as a third dimension (it was orthogonal to the plane in which the electron was orbiting the nucleus).

It was reasonably clear to me that either the size of the wave was incredibly small compared to the size of the orbital or it was oscillating in some other dimension.

I'll plug my site, which visualizes solutions to the Schrödinger equation in 1d potentials. Try the first two exercises, no math required: https://ridiculousfish.com/wavefiz/#exercises

Perhaps this, in particular "The hydrogen molecule" section https://www.feynmanlectures.caltech.edu/III_10.html

This is generally true for anything to do with matter at the microscopic level: not just chemistry, but many things about things like insulators, metals and other solids just don't make sense without quantum mechanics.

Even in the stability of solids (i.e.) why things don't pass through each) relies on the Pauli exclusion principle (and not just Coulomb repulsion as is commonly thought).

The Pauli exclusion principle is just a fancy way of saying two electrons (later extended to fermions) can't be in the same place at the same time

Yes, the point that is often missed is that Coulomb interactions aren't enough on their own.

They can, if their spins are opposite. (Speaking of 'place' specifically, different orbitals of the atom overlap in space, so in fact nothing prevents two electrons from occupying the same point in space. A striking example would be an observation that the maximum probability of finding an electron sitting on an s-orbital is inside the atom's nucleus.)

Are you forgetting a Jacobian? The maximum probability isn't inside the nucleus for an s-orbital. E.g. for hydrogen, the maximum probability for the electron is one bohr radius away from the center of the nucleus (and the expectation value of the radius is 1.5 bohr radii away).

Well let me just quote Wikipedia here: ...in three-dimensional space, the maximum probability density occurs at the location of the nucleus and not at the Bohr radius, whereas the radial probability density peaks at the Bohr radius, i.e. when plotting the probability distribution in its radial dependency.

Ah yup you're right, I read your sentence too fast, whoops. The most likely location is at the nucleus, but the most likely radius (integrating over all angles) is at 1 bohr radius.

That it is maximum at the nucleus is not of much significance. To quote a professor:[1]

> In some ways it does not provide the best description of the electron distribution, since the region around r= 0, where the wavefunction has its largest values, is a relatively small fraction of the volume accessible to the electron. Larger radii represent larger physical regions since.

If you were to do any kinds of measurements, you are most likely to find it at the Bohr radius, not closer to the nucleus.

[1] http://www.umich.edu/~chem461/QMChap7.pdf

https://www.youtube.com/watch?v=MO0r930Sn_8

Richard Feynman explaining magnets is one of the best layman explainers I've seen (in between the ranting). I honestly didn't understand why magnets worked and found this on a late night youtube binge.

(But don't search youtube for anything related to magnets, you end up amongst the perpetual motion nuts)

Edit: Just to be clear with this video (it had been a while since I last watched it), he doesn't 'explain' magnets as much as he hints at the concepts involved. I already knew about the spins being lined up etc but it was the "you can't put your hand through the chair" comment that gave me the eureka moment.

I rewatch this video constantly. It's not just about magnets, it's about epistemology and it's also the greatest masterclass on science education in my opinion. It's also one of the best distillations of the thirst for finding out that drives humans (at least some of us apparently). Flawed man, it turns out, but am thankful for at least this video if nothing else.

All humans are flawed.

Amen

Everything in the universe is flawed. (Also, what if it's our "flaws" that define who we are?)

For what it's worth, we still don't really know how magnets work; at best we can predict some of their behaviours.

What? No. This is not true. We understand 100% the physics of how magnets work.

I guess, depends on who 'we' is. (Besides, do "we" really understand quantum electrodynamics, or we just understand the math?)

Yes, speaking as a physicist, QED is perfectly understandable.

Not entirely true (that we understand magnetism). We get some things about it. But not everything.

The nature of physics is such that we never really have 100% confidence in our theories. We are always looking for things the theory under test doesn't predict correctly in the form of an observation. Which means we have to understand what we are measuring. And how we are measuring it.

All of this impacts magnetism. For example, many explanations here discuss electron "spin". Electron "spin" likely doesn't mean the electron is physically spinning.

So what is "spin" and how does it actually contribute to magnetism? And then you have a number of interesting QM properties, such as spin-orbit coupling. Remember, the original model of electrons orbiting nuclei was discarded as the electron accelerating around the nucleus would radiate all of its energy away. So classical orbital "motion" of electrons, literally a current, that should generate a magnetic field, which could couple with the spin of the electron, is not really a classical thing. It is quantum mechanical in nature.

And we really don't fully grasp QM. Some parts we think we understand and can provide some interpretation to. Other parts ... not so clear.

Again, this is why 99 years after Einstein won the Nobel prize, people are still testing relativity, and still testing fundamental/foundational QM. Look at all the work on delayed choice slit experiments[1][2], and many others.

Basically we think we have some level of understanding of QM. And we need a strong understanding of QM to understand QM phenomenon. Like magnetism.

Its not at 100% understanding yet. May never be. But there is so much more interesting science out there, that this is a good thing.

[1] https://www.popularmechanics.com/science/a22280/double-slit-...

[2] http://www.preposterousuniverse.com/blog/2019/09/21/the-noto...

My understanding is delayed slit experiments have more to do with a common folk explanation of uncertainty principle being flawed (e.g. the notion of collapse) rather that the fundamental math of QM. The later gives correct prediction.

So if you take QM math, AFAIK, it can explain all known electromagnetic phenomena.

Why does he seem so irritated at the question?

A personality quirk. Nothing sinister here.

I don't know, maybe I'm the odd man out, but I've been linked to this video tens of times and always hated it. I find Feynman comes across extremely condescending and wastes time explaining that the interviewer is too dumb to understand in a very roundabout way. One thing I've come to really respect in my CS career are people not only able but willing to distill knowledge down into an approachable way. I've come across so many people with the same attitude as seen in the video, especially in the DNS world for some reason, maybe that's why it strikes a nerve.

I completely agree that his attitude for parts of this video is cringey, but Feynman is famous for (among other things) his ability to simplify and communicate complex ideas. Feynman diagrams are the perfect example of this.

Edit: I guess my point is just that being willing and able to communicate simply and effectively is not necessarily at odds with being a condescending prick.

Except in this case he utterly failed at answering the question and went on an unrelated rant.

“What you feel in the magnet is the same force that keeps my hand from going through the chair, so the question is why does it work at a human-scale distance? The answer is that in an iron magnet all the magnetic forces in each atom are aligned. An individual atoms‘ force is too small to be felt at distance, but the combined effect of all the atoms in a magnet is large enough.”

That wasn’t so hard.

The spin of the atoms in my finger are not aligned at all, why would there be any force?

Also if it's the same force and it is much stronger when aligned, why don't magnets pass through each other? The much stronger aligned magnetic force should easy overwhelm the weaker force that keeps my hand from going through the chair.

Because as the distance becomes smaller, for unaligned magnetic fields, they stop blending into each other and become distinct fields that eventually push away each other.

As for why two magnets don't pass through each other, as they come closer eventually the alignment breaks down because both poles exist for each atom and end up repelling each other.

Of course, Paul's exclusion principle does play a role, but as long as the two objects are rigid enough you can model this mostly well enough with a magnetic dipole at each atom.

Yeah, I understand that people get satisfaction from seeing a scientist dunk on a journalist, but it doesn't seem justified in this case. Feynman's digression about distinctions between proximate and ultimate causes is interesting of course, but it strikes me that the journalist's question isn't ambiguous in this respect, and it's pretty clear what he is asking.

The question is crystal clear, and Feynman even acknowledges that it's an excellent question.

Feynman's detour is to explain to the interviewer that he can't give any satisfactory explanation beyond "the magnetic force exists and behaves like that" given that the interviewer has no advanced knowledge of physics. Trying to do so would invariably involve Feynman cheating the interviewer, causing the interviewer to believe he understood it better until he comes across the flaw in the reasoning.

But in the video he does eventually get to one, that GGGP half-mentions: It's (just about) the same force that prevents you from putting your hand through a chair even though atoms are mostly empty space, but strengthened due to how magnets are made so it works at a much larger distance.

It's a simple, relatively satisfactory explanation a layperson should understand, that provides a hook for finding more in-depth knowledge if the asker wants to.

The whole rest of it was unnecessary.

Saying that it's the same force might provide some additional info but it is not really answering the question about why there is a force.

The idea that atoms are mostly empty space is a great analog to his rubber band example. Our attempts to explain atoms in terms of electrons cleanly orbiting a nucleus gives people the wrong picture. Atoms are not mostly empty space, electrons become standing waves when part of an atom and it's not just that we cannot measure their position with accuracy, their position does not exist. The solar system metaphor for the atom has probably caused more harm than good.

You are not the odd man out, I have also seen this multiple times and had the same reaction. There is always a deeper level to explore, but good teaching both provides enlightenment and hints on where to look further.

He does explain it at around the 5:30 minute mark by saying that it is the aligned spin of the atoms within magnets that give them their peculiar strength.

I think that his leadup is an attempt to get a couple points across:

1) That we typically can explain things in terms of more basic or more 'fundamental' concepts. This does not work with magnetism since magnetism itself is a fundamental force. Attempts to explain via analogy should be avoided.

2) Even the spin explanation probably does more harm than good. A non-physicist will think of atoms spinning like a top, which is wrong and misleading.

I think he's internally dissatisfied with his own answer to the question. He's certainly a man who wanted to know more than he could ever hope to achieve. I think things like this irked him at a deep level.

You come up to him. "Hey, so magnets, these trivial things that children play with, can you explain it to me?"

His real answer would be "no. not to my satisfaction, I can't"

That isn't it, though. Feynman explains magnetism perfectly well in his lectures, he's just saying that he can't give a decent math-free answer in a few minutes to an interviewer with no science background. Any answer that short would not functionally be any better than "magnets work because of magic".

I agree with this. I found it very off putting and not what I'd expected from someone lauded as an amazing teacher.

Having said that, there is a lot to think about in his irritation. For example: the mysteries of magnets are no more mysterious than lots of other things that we take for granted and treat as entirely unmysterious. To priviledge magnets with an almost magical respect when we haven't spotted that gravity is at least as mysterious is a failure of imagination.

There's also the question 'what kind of answer would you accept'? When we can only express bafflement about a phenomenon, we're still in the prescientific myths and magic world. You can't really get to the scientific world until you can formulate some kind of question. The passage from Hitchikers about the Ultimate Question touches on something pretty profound.

Still, I think an honest expression of bafflement is an excellent beginning (or at least it's where I often find myself), and I think there may have been more sympathetic ways Feynmann could have expressed his thoughts on the topic.

I understood that differently:

https://news.ycombinator.com/item?id=22816968

Hint, the questions were:

"Now, what is it, the feeling between those two magnets?"

"There's something there, isn't there?"

"what's going on between these two bits of metal"

"What does that mean, or why are they doing that, or how are they doing that?"

I don't know what phenomena you study, but I assure you that "magnets" aren't the only topic for which the "feeling" and "what does that mean" and "why" questions would warrant the same answer.

And where answering "how" would be cheating if the answer would use some false analogy.

Wow, I think this is a problem with you. Feynman is smiling through most of his answer. His diversion at the start is just to explain to his interviewer how wide and deep the question “why” can go.

> Feynman is smiling through most of his answer.

I don't think smiling and being condescending are mutually exclusive are they?

I think the lesson of Feynman’s rant has eluded you. I’d keep studying it.

I learned the lesson of explanations going into a 'why?' rabbit hole 2 years ago. It was taught to me by my then 6 year old daughter.

That isn’t the lesson.

If a watcher doesn't understand the lesson, was it a good session? As an acolyte, why not enlighten us? Or should I just keep watching a condescending asshole avoid a question until I understand something that makes you happy?

What is the lesson?

The confusion comes from the wrong expectation: whoever called the Feynman's answer "Magnets" missed the point. I'm quite sure Feynman would not name his answer so.

One has to carefully to listen to the question he was asked and he then answers.

I wrote about that before and I link to that this time too in my other answer.

People are also missing the complete video, its not just about magnets, it’s about why imagination can be fun. Here he just demonstrates why you can’t always turn to similarities in the classical world:

https://www.youtube.com/watch?v=P1ww1IXRfTA

A reasonable perspective for sure. But I don't see it. Asked a question about the nature of magnetic force by a lay person, he saw fit to launch into a lecture about causation. He was a lecturer by trade.

Socrates, as we receive him, opened peoples' eyes about causation, too. If anyone did it like a jerk it was him. Leading you down the path of your own ideas into a contradiction, just to show you what you don't know? That's embarrassing and unhelpful. I'd rather be lectured.

Is he the friendliest explainer? Surely not. Who cares? His gifts in communicating deep ideas in science to lay people were beyond compare.

The video is great. If you feel offended by it, think about why.

I feel like the people put off by this video somehow take it personally that he didn't answer the question in a manner which they found satisfactory like he owed them a better answer. I didn't feel like he was being a jerk in the slightest. The answer he did give was rather interesting.

Did we watch the same video? I'm not in the least bit offended, I just feel like he wasted my time. If he'd just explained it, it's then up to me to research the underlying bits. Not up to him to tell me I'm too uneducated to do so.

I don't agree. I suspect you may have been put off by the beginning (before the 0:57 mark), where he may sound annoyed by the question. Personally, I don't think he was; he does agree that it's an excellent question, and continues happily from there.

His roundabout analogy about the seemingly infinite rabbit holes of "why"s makes an important point that some phenomena are not explainable in a satisfactory way without a considerable theoretical framework, and any layman-friendly analogy is ultimately going to be inaccurate.

Love the first comment on the youtube video:

"RIchard Feyman's wife: "WHY did you not take the trash out yet?!"

Richard proceeds to go on a long tirade about electromagnetic forces, gravity, string theory etc. until the wife sighs in despair and takes out the garbage herself. Again."

According to my professor, when I was taking quantum mechanics a few years back, the view that Feynman is prevented from falling through his chair by electromagnetic repulsion is somewhat antiquated. She told us that a more modern perspective puts a greater focus on the Pauli Exclusion Principle.

Of course that line of explanation falls to similar loop, re: why do fermions resist sharing state?

I would like to mention the possibility of tunneling through the chair (however small).

Indeed, and Freeman Dyson demonstrated this:

In 1966, independently of Elliott H. Lieb and Walter Thirring, Dyson and Andrew Lenard published a paper proving that the Pauli exclusion principle plays the main role in the stability of bulk matter.

https://en.wikipedia.org/wiki/Freeman_Dyson

Magnetism is a side effect of special relativity: moving charges have length contraction (depending on frame of reference) which makes them appear more/less dense and therefore an attractive/repulsive force.

Veritasium on YouTube made a much better explanation: https://youtu.be/1TKSfAkWWN0

Yeah but that doesn't explain permanent magnets, which is the subject of this theorem.

This video was a collaboration between Veritasium and Minute Physics.

They did a second one on that subject on the other channel: https://m.youtube.com/watch?v=hFAOXdXZ5TM

Indeed, that is one of my favorites; I should have pointed that out in my comment.

I like the comments:

1) "- How do magnets work? - Oh, they're just a bunch of nano-magnets"

2) "Yes, but why? Still it's a description, not an explanation"

3) "To 2: https://www.youtube.com/watch?v=MO0r930Sn_8 check it out. I really is that way"

Not always the right explanation. Magnetism of material is usually not because of charges but spin alignment of electrons. Spin is an intrinsic property of point particles, there are no moving charges (or moving anything) involved. You can have magnetism at 0K and 0 charge.

Interesting. So in the frame of reference of the electrons, the protons are moving and so closer together due to length contraction, and in the frame of reference of the protons, the electrons are moving and so closer together due to length contraction. When the cat in the video is stationary, it's in the same frame of reference as the protons, and with the electrons closer together will see a net negative charge and be attracted to the wire. I suspect that this argument is incorrect, however.

Why is it called the most deflationary finding of all time? What does deflationary mean in this context?

For me https://en.m.wikipedia.org/wiki/Magnetic_refrigeration really opened my eyes to post-classical physics. Not only is it a great way to understand entropy, but soon we may have quiet and efficient refrigerators in every home thanks to this research!

I wish there was a similar intuitive application for quantum plasma and superfluidity too, but the existence of high-temperature superconductivity seems to indicate there is none as of yet.

There is an interesting answer here with regards to how the Pauli Exclusion principle is related to magnetism.

https://physics.stackexchange.com/a/246439

As I understand it, with my limited knowledge, deeper down it involves the exchange of virtual photons between electrons. I can see how this explains repulsion.

Though how this leads to attraction and how this looks as a Feynman diagram I'm not sure.

> *"and means that classical physics cannot account for diamagnetism"

[assuming classical statistical physics assumptions, such as nothing special happens at the boundary]. The whole result is due to unrealistic boundary condition (for magnetic materials) that the Boltzmann isotropic distribution of momenta is valid at the boundary. Diamagnetism is present in classical physics, for example, electron(s) circling in magnetic field create magnetic moment opposed to the magnetic field.

The reason why electrons don't fall into the nucleus due to Coulomb attraction is QM. So from there, you can say that a lot of things are actually a QM effect.

I'm always fascinated how discoveries like this can often be simultaneously discovered only a few years apart, like what happened here.

During my classes, I always see waves going up and down to represent sound or magenetic waves. I really cannot visualize in real life. What exactly the ups and down in real time?

In sound, the waves are pressure waves; the height of the wave represents the density of the air at a point in space.

https://www.physicsclassroom.com/Class/sound/u11l1c2.gif

Magnetic waves are different. The height of the wave in a diagram of magnetic waves represents the strength and direction of a magnetic field at a point in space.

For sound, at least, the waves are not up and down, but longitudinal. Perhaps most easily illustrated using a slinky:

https://www.youtube.com/watch?v=GIkeGBXqWW0

https://www.youtube.com/watch?v=kxQj-wPePBU

For electromagnetic waves, as i understand it, there isn't actually movement up and down in space; there are oscillations in the electric and magnetic fields. Which do somehow have a spatial direction, which is why light can be polarised. I don't have an intuition for it at all!

The challenge with the longitudinal example, which is of course technically correct, is that it’s hard to map it to the spherical shells that most of these phenomena radiate into.

I don’t know if this will help you but it is how i think about it.

Just keep in mind that the waves you see plotted aren’t a direct physical model like you might find in the chapter about forces. In those topics you can directly represent a pully or a lever and depict force vectors and distances and their relationship within the system right on the page.

Waves drawn to represent sound or AC current or RF are confusing because they look like waves in the ocean so the brain just inserts that somehow. However, those waves are really a derived value that plots the field/pressure/current intensity over time (or distance). Imagine they are being drawn by a small plotter hooked to a sensor at some point in space and the up and down movement of the ink on the page is just the change in pressure/intensity over time at that spot.

There's an image on this page that depicts it as a 2D slice of reality - https://dosits.org/decision-makers/tutorials/science/what-is...

This is closer but the problem with this image is that the particles all have a laminar motion back and forth. The reality is that it's like quadrillions of superballs bouncing in random directions and these density fluctuations are only really evident in larger scale aggregations of particle motion.

Be careful not to confuse the map with the territory. These ups and downs are a graph of something, such as the pressure in a sound wave. It’s the pressure, a number, that goes up and down as the sound wave passes by.

For sound those waves are the pressure level along the line. It only really visualizes things in 1 dimension. This picture shows the relation between the wave that's usually drawn and a view of what the wave would look like if you could see the air.

https://sites.google.com/site/svgphysics/propagation-of-soun...

After working in a particularly magnetics heavy project at work an analogue that I found works better is picturing the flux lines as “fluidic” and emulating common fluid behavior. For example, having a ferromagnetic material within a magnetic field is like having a funnel in a fluid stream. Taking this analogue along with an intuitive understanding of Maxwell’s equations really gives you an intuitive understanding of magnetics for applied sciences (ie DivB = 0 means that in any bounded region the number of field lines entering = number of field lines leaving).

Of course all of this is only good up to the point you start looking at magnetics at the material science level. Then you really need to internalize it is a quantum mechanics effect and commit to learning the hard science behind it.

Veritasium has a good video on the “levels of explanation” of magnetic fields and you really need to decide how deep you want to go.

Also, it is a widely known fact that classical electrodynamics is not compatible with classical mechanics.

>"The significance of this discovery is that classical physics does not allow for such things as paramagnetism, diamagnetism and ferromagnetism and thus quantum physics are needed to explain the magnetic events.[5]"

Well, that might be true and all, but I like the following simpler explanation:

1) There is an extra dimension in space.

2) This extra dimension in space can be occupied by magnetic and other fields. They are unseen, but present when a magnetic object is present, much like radio or other electromagnetic waves are unseen, but can be present.

3) These fields, when present, exert a force on the magnetic objects they occupy, and can be used to exert force on other magnetic opjects, without the two objects ever physically touching.

Which also means that:

4) Magnetic fields are somehow intricately related to the materials they occupy, that is, the matter, at either the molecular or atomic levels...

If this is true, then one weird model for magnetism might exist as the "displacement of space"...

For example, you take a stone, you put it in some water, it displaces a little bit of that water.

But not enough to really see anything...

So now the $64,000 question:

What happens when you have a fixed ditch/gutter/trench/trough/channel/container of water, and you start to cram in stones, a whole lot of stones, such that each stone starts to displace more and more water?

Oh, and lets suppose that it's open on one side... and in that side is a much thinner open trench, which loops around to the other side, the closed side of the container?

Well, put enough stones (atoms, molecules) there, and they'll displace the water such that it flows into the small looped external open trench...

So, is a magenetic field -- actually the displacement of space?

I don't know, but there might be a case to be made for it...

Also, other observation: IF a magnetic field is in fact the displacement of space -- then this would mean that the magnetic field lines... represent a different kind of space than regular space... in other words, there are at least two kinds of space, regular space and magnetic field line space.

Then of course the next question is, how are these two types of space the same, and how are they different?

How do you make one from the other (without using a magnet!), and vice-versa?

But of course, all of the above is highly speculative...

Magnets are teleological, whereas classical mechanics is entirely efficient and material causes.

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